Download CHAPTER 3 STRUCTURES OF METAL COMPLEXES

CHAPTER 3 STRUCTURES OF METAL COMPLEXES
3.1 Introduction………………………………………………………………………………….. 1
3.2 General Characteristics of Coordination Compounds………………………………...….. 2
3.2.1
Coordination Compounds………………………………………………………… 2
3.2.2
Lewis Structures and the EAN Rule……………………………………………… 3
3.2.3
Types of Ligand Coordination……………………………………………………. 4
3.2.4
Types of Ligands…………………………………………………………………..5
3.3 Molecular Orbital and Crystal Field Theories…………………………………………….. 8
3.3.1
Molecular Orbitals of Metal-Ligand Complexes…………………………………. 8
3.3.2
Ligand Field Splitting and the Spectrochemical Series…………………………. 10
3.3.3
Crystal Field Theory…………………………………………………………….. 11
3.3.4
Electron Configurations…………………………………………………………. 12
3.3.5
Crystal Field Stabilization Energy………………………………………………. 17
3.4 Hard and Soft Acids and Bases…………………………………………………………… 19
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3.1 Introduction
In general, a metal ion exists in compounds and in aqueous solution, not as a naked ion, but
as an aggregated entity consisting typically of a central metal ion bound to a certain number of
anions or molecules. This entity is called a complex or coordination compound, and the bound
anions and molecules are termed ligands . The ligands occupy the coordination sphere of the
central metal ion and the number of bound ions and molecules associated with a given central ion
represents the coordination number of the metal ion. The metal complex may be neutral, anionic
or cationic, depending on the combination of charges on the central metal ion and the ligands.
Complexing ligands are exploited in several aqueous-based unit processes, such as dissolution,
chemical precipitation, electrodeposition, solvent extraction, ion-exchange, and adsorption.
This chapter deals with the structures of metal-ligand complexes, with emphasis on transition
metals. We begin by considering how we can understand the structures of coordination
compounds through the Lewis concept of the electron-pair bond. We then examine how
molecular orbital theory can be extended to metal-ligand complexes. Finally, some useful
generalizations are presented which should aid in the selection of ligands for specific metal ions.
3.2 General Characteristics of Coordination Compounds
3.2.1 Coordination Compounds
The serious study of coordination compounds did not begin till the end of the 18th century.
At this time the available theory of chemical bonding could not explain why compounds such as
CoCl3 and NH3, with apparently saturated valences, would combine to give a new stable
compound with stoichiometry CoC13•6NH3. Hence such compounds were termed complex,
recognition of their unknown and apparently baffling bonding mechanism. It is now recognized
that the structural chemistry of a complex is based in part on two key properties of the central
metal ion, i.e., its oxidation state, and its coordination number. Thus, in the case of
CoCl3•6NH3, the structural formula may be expressed as [Co(NH3)6]Cl3, with the following
interpretation. The oxidation state of cobalt in this complex is +3 (i.e., Co(III)) and hence three
negatively charged chloride ions are needed to satisfy this charge. On the other hand, the
ammonia molecules provide the necessary ligands to satisfy the coordination number of six; that
is, these molecules are bound directly to the metal ion.
The unique character of coordination compounds often manifests itself in the different
solution behavior of stoichiometrically similar compounds. Take for example the two
compounds with the similar stoichiometric formulas: 2KCl•HgCl2 and 2KCl•MgCl2. These two
materials dissolve in water differently:
2KCl•HgCl2 = 2K+ + HgCl42-
(3.1)
2KCl•MgCl2 = 2K+ + Mg2+ + 4Cl-
(3.2)
The first compound, 2KCl•HgCl2, is a coordination compound since the chloride ions are not
released as free ions into the aqueous phase but rather are retained in the coordination sphere of
the Hg2+ cation. Accordingly, to emphasize the intimate association of the chloride and
mercuric ions, the structural formula for this compound may be expressed as K2[HgCl4]. On the
other hand in the case of the second compound, all the chloride ions report as free ions into the
aqueous phase. Therefore this compound is a double salt (rather than a coordination compound)
and its structural formula can be legitimately expressed as 2KCl•MgCl2.
______________________________________________
EXAMPLE 3.1 Identification of bound and free chloride ions in cobaltic ammine chloride solutions
Cobaltic ammine chlorides have the general stoichiometric formula CoCl 3•nNH3. In these coordination
compounds cobalt has an oxidation state of +3 and a coordination number of 6. Also, of the potential ligands NH 3
and Cl-, ammonia molecules are bound preferentially to cobalt ions.
(a) Write down the structural formulas of the following complexes: (i) CoCl 3•6NH3, (ii) CoCl3•5NH3,
(iii) CoCl3•4NH3.
(b) When a solution of silver nitrate is added to a solution of CoCl 3•nNH3, the silver ions react with the
unbound chloride ions to give an insoluble precipitate of silver chloride (AgCl(s)). For each of the
complexes listed above, indicate the number of chloride ions precipitated.
Solution
(a) According to the problem statement, all the available NH 3 will first bind to Co3+ before Cl- can enter the
coordination sphere. Therefore, since Co3+ has a coordination number of 6, the coordination sphere of
Co3+ in CoCl3•6NH3. will consist entirely of NH3 molecules. Thus, there will be three unbound Cl - ions.
Therefore, the coordination formula is [Co(NH3)6]•Cl3. Similar considerations result in appropriate
coordination formulas for the other cobaltic ammine chloride complexes, as summarized in the table below.
(b) Since the silver ion will only react with the unbound chloride ions, it is necessary to identify the number of
free chloride ions associated with each cobaltic ammine chloride. The results of the analysis are
summarized in the table below.
Molecular
Formula
No. of
Bound NH3
CoCl3•6NH3
CoCl3•5NH3
CoCl3•4NH3
6
5
4
No. of
Bound Cl-
Coordination
No. of Cl- ions
Formula
Precipitated
_____________________________________________
0
1
2
[Co(NH3)6]Cl3
[Co(NH3)5Cl]Cl2
[Co(NH3)4Cl2]Cl
3
2
1
_____________________________________
3.2.2 Lewis Structures and the EAN Rule
Comparison of the Lewis diagrams obtained in Chapter 2 for NH3 and H2O shows that
NH3 possesses an unshared electron pair, while in the case of H2O there are two pairs of
unshared electrons. These lone electron pairs can be shared in the formation of new compounds.
Thus an ammonium (NH4+) ion forms when the electron pair on NH3 is shared with a hydrogen
ion:
H+ + :NH3= [H3N:H]+ = NH4+
(3.3)
Similarly, the oxonium ion (H3O+) results when a water molecule shares one of its two lone
electron pairs with a proton:
H+ + :OH2= [H2O:H]+ = H3O+
(3.4)
Equations 3.3 and 3.4 represent Lewis acid-base reactions. According to the Lewis
theory of acids and bases, an acid is a substance that can accept an electron pair, whereas a base
is a substance that can donate an electron pair. According to this terminology, one may refer to
an acid as an acceptor and a base as a donor. Thus, the formation of a complex or a coordination
compound can be viewed in terms of an acid-base reaction:
A
+
(Acid; acceptor)
:B
(Base; donor)
B:  A
(Complex)
=
(3.5)
In the case of metal complexes, the metal ions represent the acids while the ligands represent the
bases. Thus the formation of the cobaltic hexammine complex can be represented as:
NH3
+ 6NH3 =
Co

Co
(3.6)
H3N

NH3

3+


H3N
3+
H3N

NH3
It will be noticed that for He (Z = 2), Ne (Z = 10), and Ar (Z = 18), the atomic numbers
change in increments of 8. In contrast, for Ar (Z = 10), Kr (Z = 36), and Xe (Z = 54), the
corresponding increment is 18. This difference translates to a modification of the Lewis eightelectron rule to an Effective Atomic Number (EAN) rule for transition metal complexes.
According to the EAN rule, the ligands in the coordination sphere of a transition metal complex
must provide the necessary number of electrons that will give the central metal ion the electronic
configuration of a rare gas.
______________________________________________________________________________
EXAMPLE 3.2 The EAN rule and the structure of Co(III) hexammine
Is the coordination of Co(NH3)63+ consistent with the EAN rule?
Solution
The atomic number of Co is 27. Thus 24 electrons are associated with the Co(III) ion. Each NH 3 ligand can
offer a lone-pair, i.e., a total of 12 electrons from six ligand molecules. Therefore in the hexammine complex, the
Co(III) ion has a total of 36 electrons. This matches the electronic structure of Kr.
Alternatively, we recall from Table 2.2 that the electronic structure of Co is [Ar] 3d 74s2. Thus Co(III) has 6 valence
electrons. If we now add the 12 electrons provided by the ligands, we get a total of 18 electrons in the valence shell
of Co(III) in the complex. Thus we see that the EAN rule can be viewed, in this case, as an 18-electron rule.
____________________________________________________________________________________________
3.2.3 Types of Ligands
For most ligands the coordinating atom of the anion or molecule (i.e., the atom of the
ligand that is directly bound to the central metal ion) comes from Groups V, VI, or VII of the
Periodic Table, particularly N, P for groups V; O, S for group VI; and F, Cl, Br, I for group VII.
Table 3.1 presents a collection of common ligands and ligand atoms. We can distinguish
between monodentate ligands, characterized by the presence of only one binding site, and
polydentate ligands, which carry two or more binding sites. Examples of monodentate ligands
-
-
-
are cyanide (CN-), halide (F-, Cl , Br , I ), and ammonia (NH3). Bidentate ligands include
ethylene diamine, and acetylacetonate. Some polydentate ligands have binding atoms consisting
of different elements, e.g., glycinate (N, O), ethylenediaminetetracetate (EDTA; N,O).
In Table 3.1, certain ligands are associated with more than one ligand atom. Thus NO2
-
-
appears under both nitrogen (N) and oxygen (O), SCN is grouped with nitrogen (N) ligands as
2-
2-
well as with sulfur (S) ligands, both SO3 and S2O3 appear with the oxygen (O) and sulfur (S)
ligands. Ions or molecules which possess alternative donor atoms are given the name
ambidentate.
3.2.4 Types of Ligand Coordination
The coordination numbers encountered in metal complexes range from 2 to 9, the most
common being 6. There is only a limited number of complex ions with a coordination number of
2, and these are typically found among Group IB M(I) and Hg(II) complexes. The geometrical
arrangement of these complexes tends to be linear. In general, these bis complexes readily
accept additional ligands to give complexes with higher coordination. Three coordination in
metal complexes is also unusual.
Thus, attempts to deduce three-coordination from
-
stoichiometry can be misleading. Thus, the 3-coordinate complex CuCl3 does not exist in the
compound CsCuCl3. In fact, in this compound, Cu(II) has a coordination number of 4.
Similarly, in KCuCl3, the coordination number of Cu(II) is 6 not 3.
Two different coordination polyhedra are associated with a coordination number of 4, i.e.,
tetrahedral and square planar structures. The tendency towards the formation of a tetrahedral
structure can be rationalized in terms of steric constraints. That is, as ligands increase in charge
and/or size, there is a need for the ligands to be as far away from each other as possible. Due to
steric constraints, square planar structures are not favored by relatively large ligands. Relatively
small ligands do not favor square structures either; the ligands may be so small that twoadditional ligands may be readily accommodated below and above the square plane, giving an
octahedral complex. Thus, only a select group of metal ions can form square planar complexes.
Complexes with a coordination number of 5 are few. As with coordination number 3,
many complexes which appear from stoichiometry to be 5-coordinate may not have this
coordination at all. Examples of 5-coordination polyhedra are the trigonal bypyramid, and the
square pyramid. The coordination number 6 is the most common.
Table 3.1 Common Ligands and Ligand Atoms
Ligand Atom
Common Ligands
Carbon (C)
CN-
Nitrogen (N)
NH3, NO2 , SCN-, RNH2, R2NH, R3N
_
O
RC
(Amide), RN=O (Nitroso),
NH2
RC = N - OH (Oxime)
Oxygen (O)
_
2-
3-
H2O, OH-, O2-, NO 2 , NO3 , CO 3 , PO 4 ,
2-
2-
2-
_
S2O 3 , SO 3 , SO 4 , ClO4 , R-O-R (ether),
R-OH (Alcohol), RC=O (Ketone),
O
O (Alkyl phosphate), RC — OH (Carboxylate)
R-O
P
O-
HO
Sulfur (S)
2-
2-
HS-, S2-, SO 3 , S2O 3 , SCN-, R-S-R- (Thioether),
R-SH (Mercaptan), R-S-,
O
S
RC
(Monothiocarboxylate), RC
S-
S-
R
S
N—C
(Dialkyl dithiocarbamate)
R
S-
R— O
S
P
R— O
H2N
(Dialkyl dithiophosphate)
S-
C = S- (Thiourea)
H2N
Halogen (F, Cl, Br, I)
(Dithiocarboxylate)
F-, Cl-, Br-, I-
Table 3.2 Coordination numbers of metal complexes.
Coord. No.
2
Typical Examples
Group IB M(I) complexes, e.g.
+
M(NH3)2 , where M(I) = Cu
-
+
+
, Ag
+
MCl2 , where M(I) = Cu , Ag , Au
-
3
+
+
+
+
M(CN)2 , where M(I) = Ag , Au
Hg(II) complexes, eg., Hg(CN)2
KCu(CN)2 chain, [-CN-Cu(CN)-CN-Cu(CN)-CN-]
Triiodomercurate (II) anion, Hg I3
8
2+
2+
2+
-
3+
4 (Square)
d metal ions (e.g., Ni , Pd , Pt , Au )
4(Tetrahedral)
Large ligands (e.g., Cl , Br , I ) bonded to
-
- -
(a) small metal ions with noble gas configuration,
2
6
2+
ns np , e.g., Be
(b) metal ions with pseudo-noble gas configuration,
2
6
10
2+
3+
ns np and (n-1)d , e.g. Zn , Ga .
(c) transition metal ions which, for energetic reasons,
have no strong preference for other structures, e.g.,
2+
Co
5
7
(d )
Pentachlorocuprate (III) anion, CuCl5
33-
Pentacyanonickelate (III) anion, Ni(CN)5
6
7
8
Most Cr (III) and Co(III) complexes
Relatively small ligands (e.g., with C, N, O, F as
ligating atoms) bonded to relatively large metal cations
with high oxidation state: lanthanides, actinides, Zr, Hf, Nb, Ta,
Mo, W
3+,
9
Ln(H2O)9
_____________________________
______________________________________________
, Ln = early lanthanide metal
3.3 Molecular Orbital and Crystal Field Theories
3.3.1 Molecular Orbitals of Metal-Ligand Complexes
As discussed previously above (Section 2.5), we can view the formation of molecules as the
interaction between the valence orbitals of the constituent atoms. We shall now extend this
concept to metal-ligand complexes. Let us consider a d-metal atom, M, which forms a complex
MLn with six molecules of the ligand L. Nine atomic valence orbitals are available on the metal:
one s, three p, and five d. Suppose each ligand provides a single s-type atomic orbital, then for
the complex MLn, there will be (9+n) atomic orbitals in all. Corresponding to the n metal-ligand
bonds are n bonding and n antibonding orbitals. This leaves (9-n) orbitals, which then constitute
the nonbonding orbitals. The energy levels will be expected to increase in the order, bonding <
nonbonding < antibonding.
Figures 3.1, 3.2, and 3.3 present schematic diagrams which illustrate the molecular orbital
energy level schemes for octahedral, tetrahedral, and square planar complexes, respectively.
Figure 3.1 Energy level diagram for a sigma-bonded octahedral complex (Huheey, p.417).
Figure 3.2 Energy level diagram for a sigma-bonded tetrahedral complex (Huheey).
Figure 3.3 Energy level diagram for a sigma-bonded square planar complex (Huheey).
Application of molecular orbital theory to octahedral complexes requires the construction of
seven-centered molecular orbitals. In the case of both tetrahedral and square-planar complexes,
five-centered molecular orbitals are involved. It must be noted that the linear combination of
atomic orbitals is feasible only if the metal and ligand orbitals have the same symmetry.
The subscripts g (gerard), and u (even, ungerard) were encountered previously above. The
following additional labels are useful in describing the symmetry properties of metal-ligand
complexes. The subscript 1 indicates that the orbital does not undergo a sign change when
rotated about the Cartesian axes. The subscript 2 is used to indicate that there is no sign change
when the axis of rotation is diagonal to the Cartesian axes. For a particular energy level, the
labels a, e, and t respectively signify that, there is a single orbital, a set of two orbitals, and a set
of three orbitals. Thus the appropriate symmetry labels for the d-metal atomic orbitals are: a1g
for s, t1u for px, py, pz, t2g for dxy, dyz, dzx, and eg for dx2-y2, dz2.
It is generally the case, as shown in the above diagrams, that the ligand energy level is lower
than the metal energy levels. The implication is that the bonding molecular orbitals tend to be
ligand-like in character.
3.3.2 Ligand Field Splitting and the Spectrochemical Series
It can be seen from Figures 3.1 and 3.2 that one outcome of the presence of ligands around
the central metal ion is that the five d-type molecular orbitals are split into two groups, separated
by an energy gap identified as o for octahedral coordination and as t for tetrahedral structures.
This effect is termed ligand field splitting. In the case of the square-planar energy level
diagram...
Ligands differ in the extent to which their orbitals interact with metal orbitals. A ligand
whose orbitals interact strongly with metal orbitals is termed a strong-field ligand. Such a ligand
will produce a large ligand field splitting. On the other hand, a weak-field ligand interacts
weakly and the resulting ligand field splitting is small. Table 3.3 presents ligand field splitting
data for selected octahedral complexes (Table 7.4 SAL, p.211). It can be seen that o varies with
both the metal and ligand.
An empirically determined order of ligand fields, termed a
spectrochemical series, has been established for both ligands and metals. In the case of ligands,
the order is as follows:
I- < Br-< S2- < SCN- < Cl- < NO3- < F- < C2O42- < H2O < NCS- <
CH3CN < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO
In cases where there may be some ambiguity, the binding site on the ligand is underlined. For
metal ions, the following order has been established:
Mn2+ < V2+ < Co2+ < Fe2+ < Ni2+ < Fe3+ < Co3+ < Mn4+ <
Mo3+ < Rh3+ < Ru3+ < Pd4+ < Ir3+ < Pt4+ (SAL, p.212).
Table 3.3 Ligand field splittings (o) of ML6 complexes*
Ions
d3 Cr3+
Cl13.7
H2O
17.4
d2 Mn2+
d5 Fe3+
7.5
11.0
8.5
14.3
d6 Fe2+
d6 Co3+
d6
Rh3+
d8 Ni2+
(20.4)
7.5
Ligands
NH3
21.5
en
21.9
CN26.6
10.1
30
(35)
10.4
(20.7)
(22.9)
(23.2)
(27.0)
8.5
(34.0)
10.8
(34.6)
11.5
(32.8)
(34.8)
(45.5)
*"Values are in multiples of 1000 cm-1; entries in parentheses are for low spin complexes."
"Source: H. B. Gray, Electrons and Chemical Bonding, Benjamin, Menlo Park (1965)."
(SAL, P.211)
The empirical trends exemplified by the spectrochemical series can be rationalized with the
aid of molecular orbital theory. Three important factors are: (a) the relative energies of the
metal and ligand orbitals, (b) the degree of overlap between metal and ligand orbitals, and (c) the
extent of metal-ligand pi bonding.
______________________________________________________________________________
EXAMPLE 3.3 Metal - ligand combinations giving strong-field and weak-field complexes
Speculate on whether the following metal-ligand combinations are most likely to give weak-field or strong-field
complexes.
Solution
____________________________________________________________________________________________
3.3.3 Crystal Field Theory
It was noted above that one outcome of the presence of ligands around the central metal ion
is the splitting of the d-type orbitals into two main groups. Crystal field theory (CFT) focuses on
this characteristic feature of the energy level diagram. In the CFT approach to bonding in metalligand complexes, the development of the energy gap is viewed electrostatically: A metal
complex is considered as consisting of a central metal ion embedded in a cluster of the negative
ions and molecular dipoles which constitute the ligands. The bonding between the central metal
ion and the surrounding ligands is attributed to electrostatic interaction arising from the electric
field of the metal ion and that of the ligands. The electrostatic field emanating from the negative
charges and the negative ends of the dipoles will tend to repel the outer electrons, particularly,
the d electrons of the central metal ion. That is, the greater the proximity of a ligand to a metal
orbital, the harder it is for an electron to occupy that orbital. A consequence of this repulsion is
an increase in the energy of the d-orbitals of the central ion.
As would be expected, the geometrical arrangement (e.g., octahedral, tetrahedral, squareplanar) of the ligands around the central ion has a significant influence on the electrostatic field
experienced by the central metal ion. Let us consider an octahedral complex. We envision the
six ligand ions or molecules to be distributed along the x, y, z Cartesian axes as illustrated in
Figure 3.4a. It can be seen that the ligand-metal orbital interactions will be greatest for the dx2y2
and dz2 orbitals (i.e., the eg group) since these lie along the x, y, z axes. In contrast, there is a
smaller interaction with the dxy, dxz and dyz orbitals (i.e., the t2g group) since these lie in
between the ligands. Accordingly the eg orbitals acquire a greater energy than the t2g orbitals.
In the language of crystal field theory, this effect is termed crystal field splitting; it corresponds
to the ligand field splitting encountered previously above. Crystal field splitting for an
octahedral complex is illustrated in Figure 3.4b; the difference in energy between the e g and t2g
orbitals is denoted as o. If one considers the energy of a hypothetical complex with degenerate
d orbitals (i.e. orbitals with the same energy), then it can be demonstrated that the eg and t2g
orbitals are respectively 0.6 o and 0.4 o above and below this hypothetical energy level. A
similar analysis can also be performed for other ligand geometries, e.g., tetrahedral, and planar.
For tetrahedral complexes the ligand field effect causes a splitting of the d sublevel with the t2g
orbitals lying above the eg orbitals. In general the crystal field splitting of the tetrahedral
arrangement (t) is about a half of the corresponding octahedral value (o).
(a) Metal-ligand orbital interactions
dz2 dx 2 - y2 {eg }

E
0.6  
0.4 
dxy dxz dyz {t }
2g
(b)
Metal ion
in absence
of ligand
(c)
Metal ion
bonded to
ligand in
hogeneous
field (degenerate orbitals)
(d)
Metal ion bonded
to ligand: crystal
field splitting
Figure 3.4. Crystal field splitting for an octahedral complex
3.3.4 Electron Configurations
A major factor in working out the electron distribution in a metal-ligand complex, is the energy
level difference, . Let us return to the molecular orbital energy level diagram for octahedral
complexes shown in Figure 3.1. Each of the six ligand atoms supplies a lone pair of electrons.
The resulting twelve electrons fill up the six bonding orbitals. There can be a maximum of ten d
electrons; therefore, five orbitals are needed and these must be the next lower-lying orbitals, i.e.,
the t2g and eg* orbitals. The order in which the t2g and eg orbitals are filled by electrons, and the
extent to which electron pairing occurs, are both the combined effects of the energy level
difference o, the electrostatic energy (Eel), and the exchange energy (Eex). We recall from
Section 2.2.4 that the total energy of a given electronic configuration (Econfig) is given by:
Econfig = Eelt + Eext
(3.7)
where Eelt is the total electrostatic energy associated with Pel electron pairs and Eext (= PexEex)
is the total energy due to Pex parralel-spin electrons. For the condition o > Econfig, the leading
principle is that based on energy levels, and it is energetically more favorable to first fill up the
lower energy levels. On the other hand, when o < Econfig, the leading principle is the constraint
on electron pairing and the electronic configuration is more stable with unpaired electrons.
Table 3.4 Effect of the ligand field on the electron distribution in octahedral complexes
System
d0
d1
d2
d3
d4
d5
d6
d7
d8
d9
d10
Weak Field (High Spin)
Strong Field (Low Spin)
t2g
eg
t2g


















































eg
























The crystal field splitting can lead to modifications in the electron distributions in the five d
orbitals. As noted previously, Hund's rules require that all the d orbitals be occupied singly
before electron pairing begins, however, if the ligand field splitting is relatively large, then the eg
orbitals will be significantly higher in energy than the t2g orbitals. Under these circumstances
the lower t2g orbitals will become completely filled before occupation of the higher e g orbitals
begins. Table 3.4 illustrates the different electron distributions for low and high ligand fields in
an octahedral complex. It can be seen that the d4, d5, d6, and d7 systems differ significantly in
electron distribution, depending on whether they are subjected to a weak or a strong ligand field.
The presence of a weak field does not significantly influence electron pairing, and high-spin
complexes are said to form. On the other hand a strong field causes significant electron pairing,
and the resulting complexes are termed low-spin complexes.
____________________________________________________________________________________________
EXAMPLE 3.4 Effect of ligand field strength on the filling of d-orbitals
For a given central metal ion Mz+, determine the tendency with which the following ligands may form low-spin
complexes: F-, phenanthroline, aliphatic amine, CN -, H2O.
Solution
The relative strengths of the ligand fields are given by the spectrochemical series. That is, the ligand field strength
increases in the order: F- < H2O < amine < phenanthroline < CN-. The stronger the ligand field, the greater the
tendency towards ion-pairing, and therefore the tendency to form low-spin complexes. Thus, low-spin complexes
are expected to form in the same order as the spectrochemical series, i.e., CN- complexes are likely to be low-spin
and F- complexes high-spin.
EXAMPLE 3.5 Magnetic moments and the structure of metal complexes
The magnetic moment (mM) of a metal complex is a reflection of the number of unpaired electrons (n) that the
central metal ion contains, i.e. mM = (n(n+2))1/2 magnetons (1 Bohr magneton = 9.18 x 10 -21 gauss-cm/atom or
5564 gauss-cm/mol).
(a) Determine the magnetic moment (in Bohr magnetons) that corresponds to the following numbers of unpaired
electrons 0, 1, 2, 3, 4, 5.
(b) Determine the magnetic moment (in Bohr magnetons) of a free Fe 3+ ion.
(c) Given the following magnetic moments (shown in brackets), determine the corresponding number of unpaired
electrons for the central metal ion: (i) Fe(CN) 36 (2.3), (ii) FeF 36 (6.0), (iii) Fe(CN) 64 (0).
Solution
(a) Given that mM = (n(n + 2))1/2 magnetons, it follows that: (i) for n = 0, mM = 0; (ii) n = 1, mM = (1(1 + 2))1/2
= 1.73; (iii) n = 2, mM = (2(2 + 2))1/2 = 2.83; (iv) n = 3, mM = (3(3 + 2))1/2 = 3.87; (v) n = 4, mM = (4(4 + 2))1/2
= 4.90; (vi) n = 5, mM = (5(5 + 2))1/2 = 5.92.
(b) Fe has the electronic structure [Ar] 3d64s2. The corresponding structure of Fe3+ is [Ar] 3d54s0. The free Fe3+
ion is situated in a weak field and therefore this ion has five unpaired electrons (see Table 3.4). Thus, it follows
from part (a) that mM = 5.92 magnetons.
(c) (i) Fe(CN) 36 , mM = 2.3 magnetons. From part (a), for n = 1, mM = 1.73 magnetons; this suggests that
Fe(CN) 36 has one unpaired electron.
(ii) FeF 36 , mM = 6.0 magnetons. This suggests a structure with five unpaired electrons.
(iii) Fe(CN) 64 , mM = 0 magnetons. In this case there are no unpaired electrons.
EXAMPLE 3.6 Exchangeable electron pairs in high and low spin complexes
(a) Determine the number of exchangeable pairs for high spin and low spin complexes of (i) a d 6 ion, (ii) a d5 ion.
(b) For both ions, determine the value of Econfig.
Solution
(a)
(i) d (high spin): The relevant electronic configuration is: . Thus, 5 spin down electrons
(i.e., N = 5) and 1 spin up electron (N = 1). Thus, the number of exchangeable pairs is given by
(Equation 2.2):
6
Pex() = N(N-1)/2 = 5(4)/2 = 10
Pex = N(N-1)/2 = 1(0)/2 = 0
Thus the total number of exchangeable pairs is
Pex = Pex() + Pex = 10 + 0 = 10
6
d (low spin): The electronic configuration is:
 . Accordingly, N() = 3, N = 3.
Thus,
Pex() = Pex= N(N-1)/2 = 3(2)/2 = 3
and,
Pex = Pex() + Pex() = 3 + 3 = 6.
5
(ii) d (high spin): The electronic configuration is: . Therefore, N() = 5, N() = 0. Thus,
Pex = Pex() = N(N-1)/2 = 5(4)/2) = 10.
d (low spin):   __ __. There are 3 spin-down electrons (N()=3) and two spin-up electrons
(N() = 2). Thus,
5
Pex = [3(3-1)/2] + [2(2-1)/2] = 3+1 = 4.
EXAMPLE 3.7 Spin configuration of aquo complexes
Presented below are orbital splitting (o ) and mean pairing energy (Epair) data for aquo ions (cm-1). On the
basis of these data, speculate on the likelihood of the formation of low spin configurations.
Ion
o
20,300
d2
Ti3+
V3+
d1
Ti3+
20,300
Ion
d1
o
Epair
18,000
Epair
Solution
____________________________________________________________________________________________
3.3.5 Crystal Field Stabilization Energy
The amount of energy by which d orbitals are lowered in comparison with the hypothetical
undisturbed d orbitals is designated the crystal field stabilization energy (CFSE) of the complex.
Referring to Figure 3.4b, let us assign the zero of energy to the degenerate d levels in the
hypothetical homogeneous ligand field. Then, the energy of the eg orbitals is 0.6∆, while that of
a
b
the t2g orbitals is -0.4∆o. Thus, for a given electronic configuration t 2g eg , the net energy relative
to the degenerate levels, i.e., the crystal field stabilization energy (CFSE), is defined as:
CFSE = -(0.4a + 0.6b) ∆o = 0.4a - 0.6b)
(3.8)
Table 3.5 presents crystal field stabilization energies (in units of o) for octahedral, tetrahedral,
and square complexes.
Table 3.5 Crystal field stabilization energies for octahedral, tetrahedral, and square
complexes (in units of o).
System
Examples
Weak Field (High Spin)
Oct. Tet. Square
Strong Field (Low Spin)
Oct. Tet. Square
d0
d1
d2
d3
d4
d5
d6
d7
Ca2+, Sc3+
Ti3+ U4+
Ti2+,V3+
V2+, Cr3+
Cr2+,Mn3+
Mn2+,Fe3+,Os3+
Fe2+,Co3+,Ir3+
Co2+,Ni3+,Rh2+
0
0.4
0.8
1.2
0.6
0
0.4
0.8
0
0.27
0.54
0.36
0.18
0
0.27
0.54
0
0.51
1.02
1.45
1.22
0
0.51
1.02
0
0.4
0.8
1.2
1.6
2.0
2.4
1.8
0
0.27
0.54
0.81
1.08
0.90
0.72
0.54
0
0.57
1.02
1.45
1.96
2.47
2.90
2.67
d8
d9
d10
Ni2+,Pd2+,Pt2+,Au3+ 1.2
Cu2+,Ag2+
0.6
+
2+
2+,
Cu ,Zn ,Cd
0
Ag+,Hg2+,Ga3+
0.36
0.18
0
1.45
1.22
0
1.2
0.6
0
0.36
0.18
0
2.44
1.22
0
EXAMPLE 3.8 Crystal Field Stabilization Energies for Metal ions in Octahedral Complexes.
By assigning a value of 0.4o for each electron in a t 2g orbital, and -0.6 o for each electron in an e g orbital
(see Figure 3.4b), the crystal field stabilization energy of an octahedral complex can be calculated. Determine the
CFSE for the following octahedral complexes:
(a)
(c)
high spin d4
high spin d7
(b) low spin d4
(d) low spin d7
Solution
(a) High spin d4: In this case the d electrons experience a weak field and therefore are unpaired. Thus the electron
distribution is t 32g e 1g . Therefore if nt and ne respectively represent the number of electrons in the t 2 g and eg
orbitals, then the crystal field stabilizing energy is given by:
CFSE = nt(0.4o) + ne (-0.6o)
= (3) (0.4o) + (1) (-0.6o) = 0.6o
(b) Low spin d4: Now all the electrons are paired and they reside only in the t 2g orbitals (see Table 3.4). Thus
CFSE = (4)(0.4) o
(c) High spin d7: The corresponding electron distribution is t 52g e 2g . Thus
CFSE = (5) (0.4o) + 2(-0.6o) = 0.8o
(d) Low spin d7: the electron distribution is t 62g e 1g . Accordingly
CFSE = (6) (0.4o) + 1(-0.6o) = 1.8o
EXAMPLE 3.9 Crystal field theory and the structure of complexes
With the acid of crystal field theory rationalize the following observations.
(a) If a divalent ion from the first row of transition metals forms a low-spin complex with a coordination
number of four, the complex is most likely to be square.
(b) Metal ions from the second and third series of transition elements tend to form square complexes more
readily than those of the first.
8
9
(c) In the presence of strong ligand fields, square planar complexes are most likely to be formed by d and d
7
metal ions followed by d .
Solution
(a) We are concerned here with a coordination number of four. Thus we need to choose between a square and
a tetrahedral complex. Referring to Table 3.3, it is seen that, for a given d n configuration (1< n < 9), the
crystal field stabilization energy (CFSE) value for a low-spin square complex is higher than that for the
corresponding low-spin tetradedral complex. Thus it is reasonable to expect that square complexes would
be preferred.
(b) Since the value of ∆ increases from the first to the second and third transition series, one should expect a
corresponding increase in the stability of square complexes.
(c) Ni2+ is a d8 ion. It can be seen from Table 3.3 that square d 8 ions exhibit the highest CFSE among the
three possibilities of octahedral, tetrahedral, and square arrangements.
3.4 Hard and Soft Acids and Bases (HSAB)
Metal ions may be divided into two groups, i.e., class (a) or class (b), depending on whether
they prefer to bind to (a) the first elements in groups V, VI, and VII, i.e., N, O, F, or (b) the
second or later members of groups V, VI and VII. That is, complexes of class (a) metals follow
the stability sequence:
F- > Cl- > Br- > IO >> S > Se > Te
N >> P > As > Sb > B
On the other hand class (b) metals tend to follow the reverse order, i.e.,
I- > Br- > Cl- > FTe ~ Se ~ S >> O
P >> N
When an atom is subjected to an electric field there is a tendency for the electronic cloud
surrounding the atom to experience some distortion and an atom is said to be highly polarizable
if its electron cloud is readily distorted. The polarizability of the electron cloud increases, the
further removed it is from the atomic nucleus. Thus, large atoms or molecules which are highly
resistant towards polarization are termed hard while highly polarizable atoms are called soft.
Accordingly, N, O, and F are respectively the hardest (or least polarizable) atoms in groups V,
VI, and VII respectively. It can be stated therefore that class (a) metal ions prefer the hardest
atom of a group, whereas class (b) metal ions prefer the softest atom of a group.
Class (a) metal ions have a low polarizability while class (b) metal ions are highly
polarizable. Thus, class (a) metal ions may be identified as hard Lewis acids while class (b)
metal ions are soft Lewis acids. Therefore, the principle of hard and soft acids and bases (the
HSAB principle) may be stated thus: hard acids prefer hard bases while soft acids prefer soft
bases. Tables 3.6 and 3.7 present a classification of selected ions and molecules according to the
HSAB principle.
The most typical group (a) metal cation has a rare-gas configuration (d0 cations), e.g. Be2+,
Mg2+, Ca2+, Sr2+, Ba2+ and forms stable aqueous-soluble complexes only with ligands which
have F and O as donor atoms. On the other hand the most typical group (b) cation is
characterized by an outer shell of 18 electrons (d10), e.g. Cu+, Ag+, Zn2+, Cd2+, Hg2+.
Table 3.6 Selected Hard and Soft Bases
Hard
Borderline
Soft
H2O, OH-, F-
C6H5NH2, C5H5N,
2Br-, NO2-, SO3
R2S, RSH, RS2I-, SCN-, S2O3
32CH3COO-, PO4 , SO4
2Cl-, CO3 , ClO4 , NO3
ROH, RO-, R2O
R3P, R3As, (RO)3P
CN-, RNC, CO
C2H4, C6H6, H-, R-
NH3, RNH2, N2H4
Table 3.7 Selected Hard and Soft Acids
Hard
Borderline
H+, Li+, Na+, K+
Be2+, Mg2+, Ca2+,Sr2+,Mn2+
Fe2+, Co2+, Ni2+, Cu2+, Zn2+
Pb2+, Sn2+, Sb3+, Bi3+
Al3+, Sc3+, Ga3+, In3+
Rh3+, Ir3+, SO2,
La3+, Gd3+, Lu3+
Ru2+, Os2+, GaH3
Cr3+, Co3+, Fe3+, As3+, H3Sn3+
Soft
Cu+, Ag+, Au+, Tl+, Hg+
Pd2+, Cd2+, Pt2+, Hg2+
2CH3Hg+, Co(CN)5
Pt4+, Te4+
Si4+, Ti4+, Zr4+, Th4+, U4+
Pu4+, Ce3+, Hf4+, WO4+, Sn4+
2+
UO2 , (CH3)2Sn2+, VO2+, MoO3+
A convenient (but admittedly oversimplified) way to rationalize the observed preferential
hard-hard and soft-soft acid-base interaction is to assume that the interactions of hard acids are
primarily via ionic bonding whereas soft acids interact primarily via covalent bonding. It then
follows, from an electrostatic standpoint, that bases which are highly negatively charged and are
small in size will bind most strongly to hard acids. In the case of soft acids, the presence of d
electrons plays a critical role in the bonding interactions. These d electrons may be donated to
appropriate ligands to yield π -bonds. Consequently the most likely ligands are those whose
ligand atom (e.g. P, As, S, I) contains empty d orbitals which can accept d electrons from the
metal.
EXAMPLE 3.10 Comparison of stability constants for acid-base reactions.
Consider the following reactions:
H+ +
CH3HgOH =
H2 O
+
CH3Hg+
(1)
H+ +
CH3HgS-
= HS-
+
CH3Hg+
(2)
Speculate on the relative values of the equilibrium constants for Equations 1 and 2 (see Pearson, Science, 151, 172177 (1966)).
Solution
According to Tables 3.5 and 3.6, H+ and CH3Hg+ are hard and soft acids respectively, while OH- and S2- are
hard and soft bases respectively. In Equation 1 a hard acid (H +) reacts with a hard base (OH-) to give H2O and this
should be a favorable reaction according to the HASB principle. On the other hand, in Equation 2 the hard acid
(H+) reacts with the soft base (S2-) and this is less favorable. Thus it is expected that the equilibrium constant (K 1)
for reaction 1 would be greater that the corresponding value (K 2) for reaction 2. (In fact, it is found that log K 1 =
6.3, and log K2 = -8.4, in agreement with the predictions of the HASB principle).
EXAMPLE 3.11 Symbiotic behavior and the HSAB principle
It is observed that an acid becomes softer when it is bound to a soft base. This symbiotic effect is attributable to
the ability of the soft base to release electrons to the metal ion, thereby causing a decrease in the effective positive
charge of this ion.
(a) Compare the effective positive charge on the boron atom in BH 3 and in BF3.
(b) Discuss the likelihood of forming the complexes BH3CO and BF3CO.
(c) Speculate on the relative stabilities of the following pairs of complexes: (i) Co(NH 3)5 F2+, Co(NH3)5
I2+; (ii) Co(CN)5 I3-, Co(CN)5 F3-.
Solution
(a) It can be seen from Table 3.5 that the hydride ion (H -) is a soft base whereas the fluoride ion (F -) is a hard
base. Now, the oxidation state of boron is B3+ in both BH3 and BF3. Thus in the case of BH3, there is
partial transfer of negative charge from the soft base H - to the boron and this results in an effective charge
of less than +3 on the boron atom. On the other hand, there is little tendency for the hard base F - to lose its
electrons. Therefore it would be expected that in BF 3 the effective charge on the boron atom would not
differ significantly from +3.
(b) According to Table 3.5 CO is a soft base. Furthermore, it was found in part (a) that the effective charge on
the boron atom is lower in BH3 compared with BF3. Thus BH3 is a softer acid than BF3. Therefore the
soft base CO is more likely to bind to BH3 than to BF3.
(c) (i) From Table 4.4, Co3+ is a hard acid, NH3 is a hard base, F- is a hard base, and I- is a soft base. The
complex Co(NH3)53+ is a hard acid-hard base complex and therefore should be stable. Since NH 3 is a
hard base, the charge on the cobalt atom is expected to remain close to +3. Thus Co(NH 3)53+ will be
expected to be a hard acid. Combination of this complex with the hard base F - should therefore give a
relatively stable complex. On the other hand, the Co(NH 3)5I3+ complex involves hard acid-soft base
interaction, which is not expected to be highly favored. Thus the relative stabilities are expected to follow
the order Co(NH3)5F2+ > Co(NH3)5I2+
2is a soft acid. Consequently the complex Co(CN)5I3- is
5
based on soft acid-soft base interaction and is favorable, whereas the complex Co(CN) 5F3- is based on soft
acid-hard base interaction, which is unfavorable. Thus the relative stabilities of the complexes are expected
to follow the order Co(CN)5I3- > Co(CN)5F3-.
(ii) It can be seen from Table 3.5 that Co(CN)
FURTHER READING
1.
J. E. Huheey, E.A. Keiter, and R. L. Keiter, Inorganic Chemistry. Principles of Structure and Reactivity, 4th
ed., HarperColins, 1993.
2.
A. G. Sharpe, Inorganic Chemistry, 3rd. ed., Longman, London, 1992.
3.
G. L. Miessler and D. H. Tarr, Inorganic Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1991.
4.
D. E. Shriver, P. W. Atkins, and C. H. Langford, Inorganic Chemistry, Freeman, New York, 1990.
5.
D. W. Smith, Inorganic Substances, Cambridge, New York, 1990.
6.
B. Webster, Chemical Bonding Theory, Blackwell, Oxford, 1990.
7.
K. M. Mackay and R. A. Mackay, Introduction to Modern Inorganic Chemistry, 4th ed., Prentice Hall,
Englewood Cliffs, NJ, 1989.
8.
F. A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, 5th ed., Wiley New York, 1988.
9.
T. Moeller, Inorganic Chemistry: A Modern Introduction, Wiley, New York, 1982.
10.
K. F. Purcell and J. C. Kotz, An Introduction to Inorganic Chemistry, Sauders, Philadelphia, 1980.
11.
G. I. Brown, A New Guide to Modern Valency Theory, Longmans, London, 1967.
12.
F. Basolo and R. C. Johnson, Coordination Chemistry, 2nd ed., Science Reviews, 1986.
13.
R. G. Pearson, ed., Hard and Soft Acids and Bases, Dowden, Hutchinson and Ross, Stroudsburg, PA, 1973.
14.
R. G. Pearson, "Hard and Soft Acids and Bases, HSAB, Part I: Fundamental Principles", J. Chem. Educ., 45,
581-587 (1968); "Part II*: Underlying Theories", J. Chem. Educ., 45, 643-648 (1968).
15.
L. E. Orgel, An Introduction to Transition - Metal Chemistry: Ligand-Field Theory, 2nd ed., Wiley, New
York, 1966.